Question

The length of a rectangular deck is 4 times its width.
If the deck perimeter is 30 feet, what is the deck’s area?

Answer 1

The area of the deck is 36 square feet.

Solution:

Assume l is the length of the deck; w is its width, P is its perimeter and A is its area.

Given that length of a rectangular deck is 4 times its width

$\Rightarrow l=4w \rightarrow(1)$

Perimeter of the deck is 30 ft

$\text{Perimeter of a rectangle} = 2(\text{ length }+\text{ width })\rightarrow(2)$

On substituting all the given values in (2) we get,

$\Rightarrow30=2(4w+w) \rightarrow \frac{30}{2}=5w \rightarrow 15=5w$

On dividing we get,

$\Rightarrow w=\frac{15}{5} \rightarrow w=3 ft$

If w=3, $\rightarrow l=4\times 3=12 ft$

$\text { Area }=\text{ width } \times \text{ length }$

On substituting the values in the above formula we get,

$A=12\times3=36 \text{ square feet }$